8 8 14 triangle

Obtuse isosceles triangle.

Sides: a = 8   b = 8   c = 14

Area: T = 27.11108834235
Perimeter: p = 30
Semiperimeter: s = 15

Angle ∠ A = α = 28.95550243719° = 28°57'18″ = 0.50553605103 rad
Angle ∠ B = β = 28.95550243719° = 28°57'18″ = 0.50553605103 rad
Angle ∠ C = γ = 122.0989951256° = 122°5'24″ = 2.1310871633 rad

Height: ha = 6.77877208559
Height: hb = 6.77877208559
Height: hc = 3.87329833462

Median: ma = 10.6777078252
Median: mb = 10.6777078252
Median: mc = 3.87329833462

Inradius: r = 1.80773922282
Circumradius: R = 8.26223644719

Vertex coordinates: A[14; 0] B[0; 0] C[7; 3.87329833462]
Centroid: CG[7; 1.29109944487]
Coordinates of the circumscribed circle: U[7; -4.38993811257]
Coordinates of the inscribed circle: I[7; 1.80773922282]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151.0454975628° = 151°2'42″ = 0.50553605103 rad
∠ B' = β' = 151.0454975628° = 151°2'42″ = 0.50553605103 rad
∠ C' = γ' = 57.91100487437° = 57°54'36″ = 2.1310871633 rad

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How did we calculate this triangle?

Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 8 ; ; b = 8 ; ; c = 14 ; ;

1. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 8+8+14 = 30 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 30 }{ 2 } = 15 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 15 * (15-8)(15-8)(15-14) } ; ; T = sqrt{ 735 } = 27.11 ; ;

4. Calculate the heights of the triangle from its area.

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 27.11 }{ 8 } = 6.78 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 27.11 }{ 8 } = 6.78 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 27.11 }{ 14 } = 3.87 ; ;

5. Calculation of the inner angles of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos( alpha ) ; ; alpha = arccos( fraction{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 8**2-8**2-14**2 }{ 2 * 8 * 14 } ) = 28° 57'18" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 8**2-8**2-14**2 }{ 2 * 8 * 14 } ) = 28° 57'18" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 14**2-8**2-8**2 }{ 2 * 8 * 8 } ) = 122° 5'24" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 27.11 }{ 15 } = 1.81 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 28° 57'18" } = 8.26 ; ;




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